Common-Emitter Biasing Circuits - part II

Voltage-divider bias with emitter-bias configuration provides better stability against variations in temperature and transistor gain than the emitter-bias configuration. It is the most commonly used transistor-biasing configuration.

It is also referred to as the voltage-divider bias configuration. The input section comprises a voltage divider of resistors R_B1 and R_B2 across the supply voltage V_CC. The output section is same as the emitter-bias configuration. Figure below shows the circuit.

Voltage-divider bias with emitter-bias

The DC equivalent circuit of the voltage-divider bias with emitter-bias configuration is shown in the figure below.

DC equivalent of voltage-divider bias with emitter-bias

The circuit can be analyzed using two methods - accurate method and the approximate method. The accurate method is applicable to all circuits whereas the approximate method can be applied if under certain conditions.

Accurate Method: It makes use of Thevenin’s equivalent model of the input section as shown in Figure below. R_TH is the Thevenin’s equivalent resistance and is found by replacing the voltage source by a short circuit and calculating the resultant resistance of the circuit. R_TH is given by

V_TH is the open-circuit Thevenin’s voltage and is equal to the voltage drop across the resistor R_B2.

Thevenin’s equivalent of the input section of voltage-divider bias configuration

Figure below shows the complete circuit using Thevenin’s equivalent model.

Thevenin’s equivalent of voltage-divider bias configuration

Applying Kirchhoff’s voltage law to the base–emitter loop, we get

Substituting I_E = (β + 1)I_B, we get the expression for I_B as

If V_BE << V_TH, then

Collector–emitter voltage (V_CE) can be determined by applying Kirchhoff’s voltage law to the collector–emitter loop,

As I_C ≌ I_E,

The operating point is given by

Approximate Method: The equivalent resistance between the base terminal and the ground and is referred to as the input resistance. Its value is given by

If the value of resistance R_i is much larger than the resistance R_B2, then base current I_B is assumed to be zero and resistors R_B1 and R_B2 can be considered as series elements.

Voltage at the base terminal (V_B) is given by

The emitter voltage (V_E) is expressed as

Emitter current (I_E) is given by

As collector current (I_C) and emitter current (I_E) are approximately equal, the value of I_C is

The collector–emitter voltage (V_CE) is given by

Approximate method can be applied if the value of the input resistance R_i is equal to greater than 10 times the resistance R_B2. That is

The output circuit of the voltage-divider bias configuration is the same as that of the emitter-bias configuration. This results in the same load line for the two configurations. Load-line analysis can be carried on similar lines as to that for emitter-bias configuration.

The problem of reduction in AC gain can be solved by using a capacitor C_E in parallel with resistor R_E (as shown in figure below). The capacitor does not affect the DC analysis as it acts as an open circuit for DC voltages. For AC voltages, it tends to be short circuit thus removing the problem of AC negative feedback.

Voltage-divider bias configuration with emitter capacitor

Figure below shows the circuit for collector-to-base bias configuration (also referred to as feedback-bias). In this configuration, the base-bias voltage is obtained from the collector of the transistor instead of the collector supply voltage (V_CC). It offers good stability of the operating point against variations in temperature and transistor gain (β) due to negative feedback.

Collector-to-base bias configuration

The configuration has voltage-shunt feedback as the output voltage is fed-back in shunt to the input through base resistor (R_B).

Figure below shows the DC equivalent of the collector-to-base bias circuit. The current in the resistor R_C through supply voltage V_CC is split into two parts at the collector junction: one part flowing into the collector terminal (I_C) and the other part flowing through the base resistor (R_B). The current in resistor R_B is equal to the base current (I_B). Therefore, the current through resistor R_C is the sum of the base current (I_B) and the collector current (I_C).

DC equivalent of collector-to-base bias configuration

Applying Kirchhoff’s voltage law to the base–emitter loop, we obtain

Substituting I_C = βI_B, in the above equation we get

The value of collector current (I_C) is given by I_C = βI_B. Therefore

If the value of (β+1)R_C >> R_B, then the term (R_B + (β+1)R_C) can be approximated as βR_C and in this case the value of collector current I_C is

Applying Kirchhoff’s voltage law to the collector–emitter loop, we get

Ignoring base current (I_B) as I_B << I_C, we get

The value of the operating point for collector-to-base bias configuration is given by

The load-line analysis for collector-to-base bias can be done on similar lines to that of emitter-bias configuration.

The collector-to-base bias circuit provides stability to the operating point against variations in temperature and transistor gain (β).

The main disadvantage offered by collector-to-base bias circuit is that due to negative feedback, the AC voltage gain of the amplifier is reduced. This problem is partially solved by splitting the resistor R_B into two parts and by connecting a capacitor C_B as shown in figure below.

For AC signal, capacitor C_B acts as a short circuit and the effective base resistance R_B is reduced to half. This reduces the AC negative feedback and increases the AC voltage gain offered by the circuit.

Collector-to-base bias with capacitor to reduce AC negative feedback

Also, the base resistor (R_B) in collector-to-base bias has a small value and therefore the base current changes more rapidly with temperature. Hence, the advantage of better stability factor offered by collector-to-base bias circuit is offset by the larger variation in the base current.